Finite Group DatabasebetaFinite Group Databasebeta| order | 1296 |
| isoclinism | isoclinic class of #10619770 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C2×C3 |
No aliases for this group.
| derived | C22×C3×C9 ⋊ C3×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #10619770 |
| commutator, hypocenter | C22×C3×C9 | C3×C4 |
| Frattini | C2×C32 | D3×A4 |
| Fitting, cosocle | C23×C3×C9 | C2×C3 |
| socle | C23×C32 | C3×D3 |
| prime radical | C2×C32×A4 | D3 |
| LCS | G ▷ C22×C3×C9 | |
| UCS | C1 ◁ C2 | |
176 conjugacy classes of subgroups; only the 37 normal subgroups are shown.
This group has 176 conjugacy classes of subgroups — too many to draw. Only its 37 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 324 |
Polycyclic presentation:
2,3,2^3,3^3|a^2=c,f^3=h,f^a=f^2h^2,g^a=g^2,h^a=h^2,d^b=de,e^b=d,f^b=fg72 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1296, 774);